When continents break apart, continental crust and lithosphere are thinned until break-up is achieved and an oceanic basin is formed. The most remarkable and least understood structures associated with this process are up to 200 km wide areas of hyper-extended continental crust, which are partitioned between conjugate margins with pronounced asymmetry. Here we show, using high-resolution thermo-mechanical modelling, that hyper-extended crust and margin asymmetry are produced by steady state rift migration. We demonstrate that rift migration is accomplished by sequential, oceanward-younging, upper crustal faults, and is balanced through lower crustal flow. Constraining our models with a new South Atlantic plate reconstruction, we demonstrate that larger extension velocities may account for southward increasing width and asymmetry of these conjugate magma-poor margins. Our model challenges conventional ideas of rifted margin evolution, as it implies that during rift migration large amounts of material are transferred from one side of the rift zone to the other.